Table of Contents
Complex plane : Circle sections
In CGRAPH, a circle section is defined as a chord of a circle, whereby the starting and ending angles as well as the centre point and radius of the circle can be freely adjusted.
The function is defined uniformly above the default values for all types of area mappings, as common mappings only make sense if the same function is used. The variable names z and param (as complex numbers) as well as x and y (as the real and imaginary parts of the variable z) are permitted.
CGRAPH provides several options for input:
Input via default values
Circle sections can be defined in the area on the left-hand side.
The fields Starting angle and End angle contain the interval limits within which CGRAPH varies the angle when displaying the circle segment. The angles are entered in degrees and must not be identical. Formulas can also be entered. The angles are measured counterclockwise mathematically positive from the positive x-axis.
The Centre field specifies the centre of the circle in complex coordinates. Formulas or complex numbers can be entered.
The Radius field specifies the radius of the circle. Only real, positive values are permitted here. If formulas are used, they must return positive values. Any imaginary parts are ignored.
The Add to list button transfers the entries to the List of circle segments figures.
Graphical input
By switching the tab in the area on the right to Graphical input, it is possible to create circle segments graphically. A graphics window is displayed on the right-hand side for this purpose. The first click in the graphics window defines the centre point. A blue line then appears, which can be used to define the radius and the initial angle with the next click. An arc then appears, and the third click defines the end angle. The entry is then transferred to the List of circular segments.
If the shift key is pressed while selecting the end angle, the end angle jumps in increments of 15 degrees. This simplifies the entry of even values.
Editing circle segments
Once an entry in the list of circle segments is selected, it can be edited.
The default values of the selected entry in the list are displayed on the left-hand side and can now be changed. Once you have finished making changes, click on Change values. If you want to leave the list entry unchanged, click on Cancel change.
An entry marked in the list can be removed by clicking on the Delete entry button.
The Export… and Load from file buttons can be used to create and reload semicolon-separated CSV files. The format for this is start angle;end angle;centre point;radius Multiple circle segments can be added in one go using the Create circle cluster button. They can then also be edited.
After clicking on the Create graphic button, CGRAPH switches to the Graphics tab and shows the graphic – the original image on the left and the image above the function on the right.
The default values can be viewed in the tree on the left. If the function contains a parameter, it is displayed as a red square in the original image. Double-clicking on this square allows you to change the parameter graphically by simply moving the mouse. Clicking on the original image deactivates the parameter change. If the Shift key is pressed at the same time, the original parameter is restored. A more detailed explanation of this function can be found in the notes on changing a complex parameter in the graphic display.
The specified circle segments can be changed retrospectively – clicking on one of the values switches CGRAPH back to the tab with the default values. The graphic is adjusted as soon as the Create graphic button is clicked.